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how to you solve f^-5/(f^-3)^-1

i need help with solving the above problem


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Denise W. | Elementary / Middle / High School Math TutorElementary / Middle / High School Math T...

Hi Kristen,

Using the rule of exponents:

(xm)n = xm * n

so, (f -3)-1 = f (-3 * -1) = f 3 and so, the expression becomes:

f -5/ (f -3)-1= f -5 / f 3

The rule of exponents  xm / xn = xm-n  tells us that we can re-write the expression as:

f -5 - (3) = f -8 or

1/ f 8

since a negative exponent tells us that the term is below the division bar or the denominator of a fraction.

Hope this helps!

Brian B. | Making Math Matter...and Easy to Understand! Making Math Matter...and Easy to Underst...
5.0 5.0 (226 lesson ratings) (226)

Kristen.... think of a negative exponent as a halo on a variable or number...if the halo is positive, then it is on the proper side of the division bar....if the halo is negative, then it is out-of-place....move it to the other side of the division your question above the top variable "f" has a (-5) move it out of the numerator into the denominator and change the (-5) to a (+5)...its in the "proper place" for the f^-3 to the -1...use rule of exponents and it simplifies to f^3  ( -3 times -1 = +3).  Hence, we have eight f's in the denominator and a one in the numerator .... ANSWER is   1/f^8

 less wordy way to solve....use rules of exponents X^m/X^n  = X^(m-n)....f^-5-(3) = f^-8 = 1/f^8